Information-Theoretic Analysis of Quasi-Stationary Distribution in Domany-Kinzel Automaton
Physicists have applied matrix-product-state (MPS) techniques to characterize the quasi-stationary distribution (QSD) of the Domany–Kinzel automaton along the bond directed-percolation line, revealing a sharp information-theoretic signature across its phase transition. The study finds that in the inactive phase, surviving activity collapses into a single positional 'flock' encoding exactly one bit of mutual information, while the active phase exhibits bulk-like finite density. This approach extends MPS methods to absorbing-state systems, offering diagnostics inaccessible to conventional bulk-observable techniques.
A new preprint posted to arXiv characterizes the quasi-stationary distribution of the Domany–Kinzel stochastic cellular automaton using a matrix-product-state representation, obtained by projecting out the absorbing state and iterating the transfer matrix. This method provides the full conditional probability distribution rather than relying on moment- or sampling-based approximations, enabling direct computation of information-theoretic quantities. The spatial structure of the QSD changes sharply across the active-to-inactive phase transition: the active phase is bulk-like with finite particle density, while in the inactive phase surviving activity condenses into a single 'flock' occupying a vanishing fraction of the system. A key finding is that the bipartite mutual information of the QSD in the inactive phase equals exactly the entropy of a single binary choice — whether the flock lies to the left or right of a bipartition cut — amounting to precisely one bit of positional information. This result holds throughout the inactive phase and provides a clean information-theoretic characterization of the surviving cluster structure, from a single tight cluster deep in the inactive phase to a looser, partially filled group near criticality. The authors argue this framework generalizes MPS techniques to the projected eigenvector defining a QSD, opening a new class of diagnostics for absorbing-state phase transitions that bulk observables cannot resolve.
What's missing
As a preprint, this work has not yet undergone peer review, so its results and claims remain unvalidated by independent referees. The study does not discuss finite-size scaling in detail or quantify how the one-bit result converges with system size, which are standard caveats for numerical studies of critical phenomena.
What different sources said
- arXiv physicsCenter
Universal Information-Theoretic Structure of the Quasi-Stationary Domany--Kinzel Automaton
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